Not a direct war, thats too outdated. And not against Russia specifically.
America is trying to maintaina its global influence by ensuring it has allies throughout the world. This latest war has managed to get 2 more countries into Nato(Finland and Sweden) with popular support. At the same time, arming Ukraine in order to drain Russia from its resources+ sanctions to weaken its economy.
This way, America's allies will hold the upper hand against China's allies. Even if China's economy surpasses America's, its diplomatic/military influence will still be lacking for the foreseeable future.